Graphing Inequalities 2.6

Front

What is an inequality in mathematics?

Back

An inequality is a mathematical statement that compares two expressions and shows that one is greater than, less than, greater than or equal to, or less than or equal to the other.

Front

What does it mean for a point to be part of the solution set of an inequality?

Back

A point is part of the solution set of an inequality if it satisfies the inequality when substituted into it.

Front

How do you graph a linear inequality?

Back

To graph a linear inequality, first graph the corresponding linear equation as a boundary line. Then, shade the region that represents the solution set, using a dashed line for < or > and a solid line for ≤ or ≥.

Front

What is the difference between a solid line and a dashed line in graphing inequalities?

Back

A solid line indicates that points on the line are included in the solution set (≤ or ≥), while a dashed line indicates that points on the line are not included (< or >).

Front

What does the solution set of an inequality represent?

Back

The solution set of an inequality represents all the points that satisfy the inequality.

Front

How can you determine if a point is a solution to an inequality?

Back

To determine if a point is a solution to an inequality, substitute the coordinates of the point into the inequality and check if the statement is true.

Front

What is the significance of the boundary line in graphing inequalities?

Back

The boundary line separates the coordinate plane into two regions: one that contains the solutions to the inequality and one that does not.

Front

What are the common symbols used in inequalities?

Back

The common symbols used in inequalities are: < (less than), > (greater than), ≤ (less than or equal to), and ≥ (greater than or equal to).

Front

How do you identify the correct graph for a given inequality?

Back

To identify the correct graph for a given inequality, analyze the inequality to determine the boundary line type (solid or dashed) and the direction of shading based on the inequality sign.

Front

What is a test point in the context of inequalities?

Back

A test point is a specific point used to determine which side of the boundary line is part of the solution set.